Related papers: Structural Conditions for Full MHD Equations
We consider the ideal magnetohydrodynamics (MHD) subjected to a strong magnetic field along $x_1$ direction in three-dimensional thin domains $\Omega_\delta=\mathbb{R}^2\times(-\delta,\delta)$ with slip boundary conditions. It is well-known…
In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $…
We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been…
The magnetohydrodynamics (MHD) equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of…
We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magnetic field. Combining a recent linear instability result for…
We present a version of the conditional symmetry method in order to obtain multiple wave solutions expressed in terms of Riemann invariants. We construct an abelian distribution of vector fields which are symmetries of the original system…
In this paper, we consider the Cauchy problem of the two-dimensional regularized incompressible magnetohydrodynamics equations. The main objective of this paper is to establish the global regularity of classical solutions of the…
We study the electron magnetohydrodynamics (MHD) in two dimensional geometry, which has a rich family of steady states. In an anisotropic resistivity context, we show global in time existence of small smooth solution near a shear type…
We solve the magnetohydrodynamic (MHD) equations governing axisymmetric flows around neutron stars and black holes and found all possible solution topologies for adiabatic accretion. We divide the parameter space spanned by the conserved…
In this paper, we prove the non-uniform continuity of the data-to-solution map for the incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion in Sobolev spaces $H^s(\mathbb{R}^d)$ for all $s>0$ and $d=2,3$. Our…
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We…
We generalize here the celebrated Partial Regularity Theory of Caffarelli, Kohn and Nirenberg to the MHD equations in the framework of parabolic Morrey spaces. This type of parabolic generalization using Morrey spaces appears to be crucial…
Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark-gluon plasma in heavy-ion collisions to matters in supernovas, compact…
This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits.…
The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of "ideal barriers" that prevent global relaxation, and flow. In this paper, we…
In this paper we show how the Smoothed Particle Hydrodynamics (SPH) equations for ideal magnetohydrodynamics (MHD) can be written in conservation form with the positivity of the dissipation guaranteed. We call the resulting algorithm…
We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size…
We are concerned with the 3D incompressible Hall-magnetohydro-dynamic system (Hall-MHD). Our first aim is to provide the reader with an elementary proof of a global well-posedness result for small data with critical Sobolev regularity, in…
The evolutionary conditions for the dissipative continuous magnetohydrodynamic (MHD) shocks are studied. We modify Hada's approach in the stability analysis of the MHD shock waves. The matching conditions between perturbed shock structure…
In this paper, the Cauchy's problem for fractional MHD system with the Hall and ion-slip effects is considered. By exploring the structure of semilinear and quasilinear terms, we prove the global existence of solutions for a class of large…